Solve for $x$ and $y$ using elimination. ${-2x-3y = -32}$ ${-2x-2y = -24}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-2x-3y = -32}$ $2x+2y = 24$ Add the top and bottom equations together. $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-2x-3y = -32}\thinspace$ to find $x$ ${-2x - 3}{(8)}{= -32}$ $-2x-24 = -32$ $-2x-24{+24} = -32{+24}$ $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ You can also plug ${y = 8}$ into $\thinspace {-2x-2y = -24}\thinspace$ and get the same answer for $x$ : ${-2x - 2}{(8)}{= -24}$ ${x = 4}$